The combined equation of the bisectors of the angle between the lines represented by (x2+y2) √3=4 x y is

Question

The combined equation of the bisectors of the angle between the lines represented by (x2+y2) √3=4 x y is (A) y2-x2=0 (B) x y=0 (C) x2+y2=2 x y (D) (x2-y2/√3)=(x y/2)

Tardigrade Admin · Accepted Answer

√3 x2-4 x y+√3 y2=0 Pair of angle bisectors are (x2-y2/√3-√3)=(x y/(-2)) ⇒ x2-y2=0 ⇒ y2-x2=0

Q. The combined equation of the bisectors of the angle between the lines represented by $(x^{2} + y^{2}) 3 = 4 x y$ is

$y^{2} - x^{2} = 0$

$x y = 0$

$x^{2} + y^{2} = 2 x y$

$\frac{x ^{2} - y ^{2}}{3} = \frac{x y}{2}$

$3 x^{2} - 4 x y + 3 y^{2} = 0$
Pair of angle bisectors are $\frac{x ^{2} - y ^{2}}{3 - 3} = \frac{x y}{( - 2 )}$
$\Rightarrow x^{2} - y^{2} = 0 \Rightarrow y^{2} - x^{2} = 0$

Q. The combined equation of the bisectors of the angle between the lines represented by (x2+y2)3​=4xy is

y2−x2=0

xy=0

x2+y2=2xy

3​x2−y2​=2xy​